If (a_n=3n+2), find the sum of the first (5) terms.
Answer and explanation
Correct answer: (55)
The governing idea is summing the specified initial terms of an arithmetic progression. The formula aₙ = 3n + 2 gives a₁ = 3(1) + 2 = 5, a₂ = 8, a₃ = 11, a₄ = 14, and a₅ = 17. These terms form an AP with first term 5 and common difference 3. Their sum is 5 + 8 + 11 + 14 + 17 = 55. Equivalently, S₅ = 5[2(5) + (5−1)3] ÷ 2 = 55. Hence option B is correct. The distractors commonly come from using n = 0 initially, omitting a term, or making an arithmetic error.
Frequently asked questions
What is the correct answer to this question?
(55)
Why is this the correct answer?
The governing idea is summing the specified initial terms of an arithmetic progression. The formula aₙ = 3n + 2 gives a₁ = 3(1) + 2 = 5, a₂ = 8, a₃ = 11, a₄ = 14, and a₅ = 17. These terms form an AP with first term 5 and common difference 3. Their sum is 5 + 8 + 11 + 14 + 17 = 55. Equivalently, S₅ = 5[2(5) + (5−1)3] ÷ 2 = 55. Hence option B is correct. The distractors commonly come from using n = 0 initially, omitting a term, or making an arithmetic error.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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